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QuestionA random sample was taken of 20 patients admitted to a hospital witha certain diagnosis. The lengths of stays in days for the 20 patients were4, 2, 4, 7, 1, 5, 3, 2, 2, 45, 2, 5, 3, 1, 4, 3, 1, 1, 3a Calculate a 95% confidence interval (use the methodSE) for the mean length of hospital stay. Is your answer reasonable? What underlying assumptions were required for this method and are they reasonable?b. Calculate a 95% percentile bootstrap interval and interpret.c. Refer to the previous problem. Take logs of the data (base “e”) Calculate a 95% confidence interval for the mean of the log length of stay.d. Take antilogs (exponential) of the endpoints of the confidence interval found inpart a.. Explain why that is a 95% confidence interval for the median length of stay if the data is lognormally distributed (lognormally distributed is when the logarithm of the data points has a normal distribution). Technically, under the lognormal assumption, is the confidence interval that you found in this equation also a confidence interval for the mean length of stay?MathStatistics and Probability

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